Fuzzy classification with distance-based depth prototypes: High-dimensional unsupervised and/or supervised problems

Abstract

Supervised and unsupervised classification is crucial in many areas where different types of data sets are common, such as biology, medicine, or industry, among others. A key consideration is that some units are more typical of the group they belong to than others. For this reason, fuzzy classification approaches are necessary. In this paper, a fuzzy supervised classification method, which is based on the construction of prototypes, is proposed. The method obtains the prototypes from an objective function that includes label information and a distance-based depth function. It works with any distance and it can deal with data sets of a wide nature variety. It can further be applied to data sets where the use of Euclidean distance is not suitable and to high-dimensional data (data sets in which the number of features is larger than the number of observations , often written as ). In addition, the model can also cope with unsupervised classification, thus becoming an interesting alternative to other fuzzy clustering methods. With synthetic data sets along with high-dimensional real biomedical and industrial data sets, we demonstrate the good performance of the supervised and unsupervised fuzzy proposed procedures.